Can anyone suggest an audio program (preferably for Linux) that can
     help
     isolate Biden's voice? Computery techniques I could use, or you
     could
     use, to help figure out what he's whispering?

   Do you have software development skills?
   The best solution is likely to train or fine tune something like
   Mozilla DeepSpeech around obstructed human whispers.
   To do that you'll need a way of generating similar whispers.  This
   means simulating cover noise overlayed on the DeepSpeech training data.